Number Base Converter

Type a number in the box above and it appears at once in binary, octal, decimal and hexadecimal, plus one more base of your choice from 2 to 36. Leave From on Auto and the tool reads 0x as hex, 0b as binary and 0o as octal; anything else is read as decimal. Each Copy button copies the plain value, without the grouping spaces or commas.

This number base converter does the maths exactly. Whole numbers use big integers, so a 40-digit value converts with no rounding at all. Negative numbers and fractions work too, and the panels below show two's complement, the working, the bits, the IEEE 754 float form and text as bytes. It all runs in your browser.

A base, or radix, is how many digits a number system uses. Decimal has ten (0 to 9), binary has two (0 and 1), octal has eight (0 to 7) and hexadecimal has sixteen: 0 to 9, then A to F for ten to fifteen. Higher bases keep going through the alphabet, so base 36 ends at Z.

Each position is worth the base times the position to its right. In binary the positions are worth 1, 2, 4, 8, 16 and so on; in hex they are 1, 16, 256 and 4096. A number base converter only rewrites the same amount with a different set of position values. Some values worth knowing:

To read binary, write the place values over the digits from right to left (1, 2, 4, 8, 16, 32 and so on) and add up the ones that sit over a 1. Take 101101: the ones are under 32, 8, 4 and 1, so the value is 45. With 11111111 every place is set: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.

Type a binary value with 0b in front, or set From to Binary (2), and the Decimal row shows the answer. Used as a binary to decimal converter, the tool has no length limit: a 256-bit pattern comes out as an exact whole number, not a rounded one in scientific notation.

Going the other way, divide by 2 again and again and write down each remainder. For 156: 156 ÷ 2 = 78 remainder 0, 78 ÷ 2 = 39 remainder 0, 39 ÷ 2 = 19 remainder 1, 19 ÷ 2 = 9 remainder 1, 9 ÷ 2 = 4 remainder 1, 4 ÷ 2 = 2 remainder 0, 2 ÷ 2 = 1 remainder 0 and 1 ÷ 2 = 0 remainder 1. Read the remainders from the bottom up: 10011100.

The Step by step panel prints exactly these lines for any number you type in decimal, so you can check homework or find where a hand calculation went wrong. For decimal to binary with a fraction, it adds a second list that multiplies the fraction part by 2 and keeps each whole part as the next digit.

Hexadecimal packs four bits into one digit, which is why memory addresses, colour codes and byte dumps use it. For hex to decimal, multiply each digit by its place value of 1, 16, 256 or 4096 and add: 2F is 2 × 16 + 15 = 47, and 1A3 is 1 × 256 + 10 × 16 + 3 = 419.

For decimal to hex, divide by 16 and keep the remainders, writing 10 to 15 as A to F. 255 ÷ 16 = 15 remainder 15 (F), then 15 ÷ 16 = 0 remainder 15 (F), so 255 is FF. With From set to Hexadecimal (16), a leading # is accepted, so a web colour such as #1E90FF can be pasted straight in; the Color Picker shows the same colour in other formats.

Because 16 is 2 to the power of 4, every hex digit stands for exactly four bits. To go from binary to hex, split the bits into groups of four from the right, pad the leftmost group with zeros, and swap each group for its digit: 1101 0110 becomes D6, and 101101 becomes 0010 1101, which is 2D.

Group digits does the first half for you: binary is shown in blocks of four bits, hex in blocks of four digits and decimal with commas. Octal works the same way with groups of three bits, since 8 is 2 to the power of 3.

For octal to decimal, the place values are 1, 8, 64 and 512. The Unix file permission 755 is 7 × 64 + 5 × 8 + 5 = 493, and each octal digit is three permission bits: 7 is 111 (read, write, execute) and 5 is 101 (read and execute).

Octal is rarer than hex today, but it still appears in file permissions and in programming languages that write it as 0o755. Type it with that 0o prefix and Auto reads it as octal.

The Step by step panel shows how each answer was reached. When the input is not decimal, it first writes each digit times the base to the power of its position. For binary to decimal with steps, type 0b1011 and the panel shows 1 × 2^3 + 0 × 2^2 + 1 × 2^1 + 1 × 2^0, then = 11 in decimal. Digits after the point use negative powers, so binary 0.1 is 1 × 2^-1, which is 0.5.

When the target base is not decimal either, the working carries on from the decimal value: repeated division for the whole part and repeated multiplication for the fraction, with up to 12 fraction steps. By default the target is binary for decimal input and decimal for everything else.

The same panel works for every pair of bases from 2 to 36, so it doubles as a number base calculator with steps for the less common cases too. Converting 0o755 to base 5, for example, shows the positional sum to 493 first and then the divisions by 5, ending in 3433.

It lists up to 40 positional terms and 70 division lines, which covers anything you would work through by hand. The result rows above are never shortened.

A fraction has a finite number of digits in a base only when every prime factor of its denominator is also a factor of the base. One tenth is fine in decimal, but 10 has a factor of 5 and 2 does not, so 0.1 in binary repeats forever: 0.000110011001100… The tool finds the loop and shows it as 0.0(0011), where the digits in brackets repeat. In hex the same value is 0.1(9), and in octal 0.0(6314).

Because this number base converter uses exact fractions, the repeat is found reliably instead of guessed from rounded digits. When a pattern is longer than the Fraction digits setting (8, 16, 32 or 64), the result stops and ends in “…”. Values such as 0.5, 0.25 and 0.375 end cleanly in binary as 0.1, 0.01 and 0.011.

Computers store negative whole numbers in two's complement. By hand, write the positive value in the chosen width, flip every bit and add 1. For -42 in 8 bits: 42 is 00101010, flipped it is 11010101, and adding 1 gives 11010110, or D6 in hex.

The Signed numbers panel works as a two's complement calculator: choose a width of 8, 16, 32, 64 or 128 bits and it shows the bit pattern and its hex form, or tells you the number does not fit. As signed values, 8 bits hold -128 to 127 and 16 bits hold -32,768 to 32,767.

It also works backwards. Type a pattern in binary, octal or hex and the panel reads it as a signed value of the chosen width: at 8 bits, 0xFF is -1 (unsigned 255) and 0x80 is -128. In the main rows, a negative number keeps its minus sign, as on paper.

For whole numbers below 2^64, the Bits and their values panel draws every bit as a cell, numbered from 0 on the right, in rows of 16. Set bits are blue, and hovering a cell shows its worth: bit 7 is 2^7, or 128. The pattern is padded to whole bytes, so 5 appears as 00000101, which makes flags and masks easy to check.

Most programming languages keep decimals as IEEE 754 floating point numbers. The IEEE 754 panel shows your number as a 32-bit float (1 sign bit, 8 exponent bits, 23 fraction bits) and a 64-bit double (1, 11 and 52), with the three parts coloured and the hex form of each.

This is where the repeating binary of 0.1 matters. A 32-bit float keeps only 24 significant bits, so 0.1 is stored as 3DCCCCCD, which actually holds 0.10000000149011612. The 64-bit form, 3FB999999999999A, is much closer but still not exact, which is why 0.1 + 0.2 is not exactly 0.3 in many languages.

The Text to binary and back panel turns words into UTF-8 bytes and shows each byte in binary, hex and decimal. “Hi” becomes 01001000 01101001, which is 48 69 in hex and 72 105 in decimal. Accented letters and emoji take two to four bytes, so é is C3 A9.

Paste binary such as 01001000 01101001, or hex such as 48 69, into the second box to read it back as text. Binary is read in groups of eight bits and hex in pairs; spaces between bytes are optional.

Convert many at once turns the number base converter into a batch tool. Paste one number per line; each line is read in the From base (or detected line by line on Auto), converted to the base you pick and listed beside the original. Lines that are not valid numbers are marked “not valid” instead of stopping the list.

Up to 5,000 lines are converted and the first 200 are previewed. The CSV button saves them all as converted-numbers.csv, ready for a spreadsheet.

Beyond the four everyday bases, the last row converts to any base from 2 to 36. Base 36 is handy for short IDs: 1,000,000 in decimal is LFLS in base 36. The input can be in any of these bases too, in capitals or small letters.

Many converters use ordinary floating point numbers and quietly round anything above 2^53. This number base converter online uses JavaScript BigInt for whole numbers, so huge values keep every digit. Try 2^128 - 1 in hex, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and the Decimal row shows all 39 digits of 340282366920938463463374607431768211455.

This number base converter runs entirely in your browser with JavaScript. Nothing you type is uploaded or logged. Only your display settings are saved, in this browser's local storage, and clearing your site data removes them.

Working with other encodings? Try the Base64 tool, URL Encode for links, the Hash Generator for MD5 and SHA-256 fingerprints, and the Timestamp Converter for Unix times.